Folks doing cryptography in the 1950s didn’t need to be mathmaticians. They simply needed to understand a particular set of algorithms (that happen to be derived from math theorems).

The https://www.safaribooksonline.com/oriole/probabilistic-programming-from-scratch-1-a-b-testing-with-approximate-bayesian-computation teaches you what a cryptanalyst learned in cryptographics 101, circa 1950. Little had changed since 1943.

If I said this a few years ago, Id be shot. Now its all laid out…

The teacher is good. He’s a total natural. When he says that the hardness of the problem is basically how wide is the distribution of guess, for the count fairs jar of coins, he is exactly right. now one gleans just why, back in 1944 colossus, one is driving the uncertainty out to the very extremes of the deviations … so that one has maximally learned from the simulated data, from guesses, how to minimize the variance from all the trials. That’s a fancy way of saying … the data now supports the conclusion!

In 1943, with ships sinking (at obvious cost) and time being of the essence, one needed means to decide which path to take (when attacking cryptograms). one sees how such entirely qualitative factors could be added to an otherwise quantitative search, to help direct the machine search.

The following address tunny (rather than enigma); but the general principle is the same!